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annotate src/DLD-FUNCTIONS/svd.cc @ 11523:fd0a3ac60b0e
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author | John W. Eaton <jwe@octave.org> |
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date | Fri, 14 Jan 2011 05:47:45 -0500 |
parents | eec74ee00b32 |
children | 06c80c90a246 |
rev | line source |
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2928 | 1 /* |
2 | |
11523 | 3 Copyright (C) 1996-2011 John W. Eaton |
2928 | 4 |
5 This file is part of Octave. | |
6 | |
7 Octave is free software; you can redistribute it and/or modify it | |
8 under the terms of the GNU General Public License as published by the | |
7016 | 9 Free Software Foundation; either version 3 of the License, or (at your |
10 option) any later version. | |
2928 | 11 |
12 Octave is distributed in the hope that it will be useful, but WITHOUT | |
13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
15 for more details. | |
16 | |
17 You should have received a copy of the GNU General Public License | |
7016 | 18 along with Octave; see the file COPYING. If not, see |
19 <http://www.gnu.org/licenses/>. | |
2928 | 20 |
21 */ | |
22 | |
23 #ifdef HAVE_CONFIG_H | |
24 #include <config.h> | |
25 #endif | |
26 | |
27 #include "CmplxSVD.h" | |
28 #include "dbleSVD.h" | |
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29 #include "fCmplxSVD.h" |
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30 #include "floatSVD.h" |
2928 | 31 |
32 #include "defun-dld.h" | |
33 #include "error.h" | |
34 #include "gripes.h" | |
35 #include "oct-obj.h" | |
36 #include "pr-output.h" | |
37 #include "utils.h" | |
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38 #include "variables.h" |
2928 | 39 |
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40 static int Vsvd_driver = SVD::GESVD; |
10601 | 41 |
2928 | 42 DEFUN_DLD (svd, args, nargout, |
3548 | 43 "-*- texinfo -*-\n\ |
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44 @deftypefn {Loadable Function} {@var{s} =} svd (@var{a})\n\ |
3372 | 45 @deftypefnx {Loadable Function} {[@var{u}, @var{s}, @var{v}] =} svd (@var{a})\n\ |
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46 @deftypefnx {Loadable Function} {[@var{u}, @var{s}, @var{v}] =} svd (@var{a}, @var{econ})\n\ |
3372 | 47 @cindex singular value decomposition\n\ |
48 Compute the singular value decomposition of @var{a}\n\ | |
49 @tex\n\ | |
50 $$\n\ | |
6620 | 51 A = U S V^H\n\ |
3372 | 52 $$\n\ |
53 @end tex\n\ | |
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54 @ifnottex\n\ |
3372 | 55 \n\ |
56 @example\n\ | |
6620 | 57 A = U*S*V'\n\ |
3372 | 58 @end example\n\ |
10840 | 59 \n\ |
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60 @end ifnottex\n\ |
3372 | 61 \n\ |
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62 The function @code{svd} normally returns only the vector of singular values.\n\ |
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63 When called with three return values, it computes\n\ |
3372 | 64 @tex\n\ |
65 $U$, $S$, and $V$.\n\ | |
66 @end tex\n\ | |
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67 @ifnottex\n\ |
3372 | 68 U, S, and V.\n\ |
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69 @end ifnottex\n\ |
3372 | 70 For example,\n\ |
71 \n\ | |
72 @example\n\ | |
73 svd (hilb (3))\n\ | |
74 @end example\n\ | |
75 \n\ | |
76 @noindent\n\ | |
77 returns\n\ | |
2928 | 78 \n\ |
3372 | 79 @example\n\ |
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80 @group\n\ |
3372 | 81 ans =\n\ |
82 \n\ | |
83 1.4083189\n\ | |
84 0.1223271\n\ | |
85 0.0026873\n\ | |
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86 @end group\n\ |
3372 | 87 @end example\n\ |
88 \n\ | |
89 @noindent\n\ | |
90 and\n\ | |
91 \n\ | |
92 @example\n\ | |
93 [u, s, v] = svd (hilb (3))\n\ | |
94 @end example\n\ | |
95 \n\ | |
96 @noindent\n\ | |
97 returns\n\ | |
98 \n\ | |
99 @example\n\ | |
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100 @group\n\ |
3372 | 101 u =\n\ |
2928 | 102 \n\ |
3372 | 103 -0.82704 0.54745 0.12766\n\ |
104 -0.45986 -0.52829 -0.71375\n\ | |
105 -0.32330 -0.64901 0.68867\n\ | |
106 \n\ | |
107 s =\n\ | |
108 \n\ | |
109 1.40832 0.00000 0.00000\n\ | |
110 0.00000 0.12233 0.00000\n\ | |
111 0.00000 0.00000 0.00269\n\ | |
112 \n\ | |
113 v =\n\ | |
114 \n\ | |
115 -0.82704 0.54745 0.12766\n\ | |
116 -0.45986 -0.52829 -0.71375\n\ | |
117 -0.32330 -0.64901 0.68867\n\ | |
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118 @end group\n\ |
3372 | 119 @end example\n\ |
120 \n\ | |
121 If given a second argument, @code{svd} returns an economy-sized\n\ | |
122 decomposition, eliminating the unnecessary rows or columns of @var{u} or\n\ | |
123 @var{v}.\n\ | |
124 @end deftypefn") | |
2928 | 125 { |
126 octave_value_list retval; | |
127 | |
128 int nargin = args.length (); | |
129 | |
130 if (nargin < 1 || nargin > 2 || nargout == 2 || nargout > 3) | |
131 { | |
5823 | 132 print_usage (); |
2928 | 133 return retval; |
134 } | |
135 | |
136 octave_value arg = args(0); | |
137 | |
5275 | 138 octave_idx_type nr = arg.rows (); |
139 octave_idx_type nc = arg.columns (); | |
2928 | 140 |
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141 if (arg.ndims () != 2) |
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142 { |
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143 error ("svd: only valid for matrices"); |
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144 return retval; |
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145 } |
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146 |
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147 bool isfloat = arg.is_single_type (); |
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148 |
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149 SVD::type type = ((nargout == 0 || nargout == 1) |
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150 ? SVD::sigma_only |
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151 : (nargin == 2) ? SVD::economy : SVD::std); |
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152 |
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153 SVD::driver driver = static_cast<SVD::driver> (Vsvd_driver); |
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154 |
4478 | 155 if (nr == 0 || nc == 0) |
2928 | 156 { |
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157 if (isfloat) |
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158 { |
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159 switch (type) |
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160 { |
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161 case SVD::std: |
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162 retval(2) = FloatDiagMatrix (nc, nc, 1.0f); |
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163 retval(1) = FloatMatrix (nr, nc); |
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164 retval(0) = FloatDiagMatrix (nr, nr, 1.0f); |
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165 break; |
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166 case SVD::economy: |
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167 retval(2) = FloatDiagMatrix (0, nc, 1.0f); |
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168 retval(1) = FloatMatrix (0, 0); |
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169 retval(0) = FloatDiagMatrix (nr, 0, 1.0f); |
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170 break; |
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171 case SVD::sigma_only: default: |
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172 retval(0) = FloatMatrix (0, 1); |
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173 break; |
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174 } |
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175 } |
4478 | 176 else |
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177 { |
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178 switch (type) |
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179 { |
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180 case SVD::std: |
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181 retval(2) = DiagMatrix (nc, nc, 1.0); |
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182 retval(1) = Matrix (nr, nc); |
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183 retval(0) = DiagMatrix (nr, nr, 1.0); |
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184 break; |
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185 case SVD::economy: |
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186 retval(2) = DiagMatrix (0, nc, 1.0); |
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187 retval(1) = Matrix (0, 0); |
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188 retval(0) = DiagMatrix (nr, 0, 1.0); |
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189 break; |
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190 case SVD::sigma_only: default: |
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191 retval(0) = Matrix (0, 1); |
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192 break; |
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193 } |
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194 } |
2928 | 195 } |
196 else | |
197 { | |
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198 if (isfloat) |
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199 { |
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200 if (arg.is_real_type ()) |
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201 { |
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202 FloatMatrix tmp = arg.float_matrix_value (); |
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203 |
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204 if (! error_state) |
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205 { |
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206 if (tmp.any_element_is_inf_or_nan ()) |
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207 { |
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208 error ("svd: cannot take SVD of matrix containing Inf or NaN values"); |
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209 return retval; |
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210 } |
4478 | 211 |
10601 | 212 FloatSVD result (tmp, type, driver); |
4478 | 213 |
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214 FloatDiagMatrix sigma = result.singular_values (); |
4478 | 215 |
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216 if (nargout == 0 || nargout == 1) |
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217 { |
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218 retval(0) = sigma.diag (); |
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219 } |
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220 else |
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221 { |
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222 retval(2) = result.right_singular_matrix (); |
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223 retval(1) = sigma; |
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224 retval(0) = result.left_singular_matrix (); |
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225 } |
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226 } |
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227 } |
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228 else if (arg.is_complex_type ()) |
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229 { |
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230 FloatComplexMatrix ctmp = arg.float_complex_matrix_value (); |
4478 | 231 |
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232 if (! error_state) |
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233 { |
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234 if (ctmp.any_element_is_inf_or_nan ()) |
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235 { |
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236 error ("svd: cannot take SVD of matrix containing Inf or NaN values"); |
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237 return retval; |
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238 } |
4478 | 239 |
10601 | 240 FloatComplexSVD result (ctmp, type, driver); |
4478 | 241 |
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242 FloatDiagMatrix sigma = result.singular_values (); |
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244 if (nargout == 0 || nargout == 1) |
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245 { |
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246 retval(0) = sigma.diag (); |
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247 } |
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248 else |
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249 { |
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250 retval(2) = result.right_singular_matrix (); |
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251 retval(1) = sigma; |
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252 retval(0) = result.left_singular_matrix (); |
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253 } |
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254 } |
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255 } |
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256 } |
4478 | 257 else |
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258 { |
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259 if (arg.is_real_type ()) |
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260 { |
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261 Matrix tmp = arg.matrix_value (); |
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262 |
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263 if (! error_state) |
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264 { |
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265 if (tmp.any_element_is_inf_or_nan ()) |
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266 { |
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267 error ("svd: cannot take SVD of matrix containing Inf or NaN values"); |
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268 return retval; |
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269 } |
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270 |
10601 | 271 SVD result (tmp, type, driver); |
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272 |
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273 DiagMatrix sigma = result.singular_values (); |
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274 |
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275 if (nargout == 0 || nargout == 1) |
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276 { |
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277 retval(0) = sigma.diag (); |
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278 } |
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279 else |
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280 { |
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281 retval(2) = result.right_singular_matrix (); |
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282 retval(1) = sigma; |
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283 retval(0) = result.left_singular_matrix (); |
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284 } |
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285 } |
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286 } |
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287 else if (arg.is_complex_type ()) |
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288 { |
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289 ComplexMatrix ctmp = arg.complex_matrix_value (); |
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290 |
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291 if (! error_state) |
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292 { |
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293 if (ctmp.any_element_is_inf_or_nan ()) |
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294 { |
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295 error ("svd: cannot take SVD of matrix containing Inf or NaN values"); |
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296 return retval; |
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297 } |
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298 |
10601 | 299 ComplexSVD result (ctmp, type, driver); |
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300 |
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301 DiagMatrix sigma = result.singular_values (); |
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302 |
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303 if (nargout == 0 || nargout == 1) |
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304 { |
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305 retval(0) = sigma.diag (); |
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306 } |
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307 else |
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308 { |
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309 retval(2) = result.right_singular_matrix (); |
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310 retval(1) = sigma; |
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311 retval(0) = result.left_singular_matrix (); |
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312 } |
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313 } |
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314 } |
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315 else |
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316 { |
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317 gripe_wrong_type_arg ("svd", arg); |
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318 return retval; |
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319 } |
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320 } |
2928 | 321 } |
322 | |
323 return retval; | |
324 } | |
325 | |
326 /* | |
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327 |
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328 %!assert(svd ([1, 2; 2, 1]), [3; 1], sqrt (eps)); |
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329 |
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330 %!test |
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331 %! [u, s, v] = svd ([1, 2; 2, 1]); |
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332 %! x = 1 / sqrt (2); |
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333 %! assert (u, [-x, -x; -x, x], sqrt (eps)); |
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334 %! assert (s, [3, 0; 0, 1], sqrt (eps)); |
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335 %! assert (v, [-x, x; -x, -x], sqrt (eps)); |
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336 |
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337 %!test |
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338 %! a = [1, 2, 3; 4, 5, 6]; |
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339 %! [u, s, v] = svd (a); |
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340 %! assert (u * s * v', a, sqrt (eps)); |
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341 |
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342 %!test |
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343 %! a = [1, 2; 3, 4; 5, 6]; |
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344 %! [u, s, v] = svd (a); |
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345 %! assert (u * s * v', a, sqrt (eps)); |
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346 |
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347 %!test |
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348 %! a = [1, 2, 3; 4, 5, 6]; |
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349 %! [u, s, v] = svd (a, 1); |
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350 %! assert (u * s * v', a, sqrt (eps)); |
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351 |
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352 %!test |
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353 %! a = [1, 2; 3, 4; 5, 6]; |
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354 %! [u, s, v] = svd (a, 1); |
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355 %! assert (u * s * v', a, sqrt (eps)); |
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356 |
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357 %!assert(svd (single([1, 2; 2, 1])), single([3; 1]), sqrt (eps('single'))); |
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358 |
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359 %!test |
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360 %! [u, s, v] = svd (single([1, 2; 2, 1])); |
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361 %! x = single (1 / sqrt (2)); |
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362 %! assert (u, [-x, -x; -x, x], sqrt (eps('single'))); |
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363 %! assert (s, single([3, 0; 0, 1]), sqrt (eps('single'))); |
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364 %! assert (v, [-x, x; -x, -x], sqrt (eps('single'))); |
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365 |
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366 %!test |
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367 %! a = single([1, 2, 3; 4, 5, 6]); |
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368 %! [u, s, v] = svd (a); |
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369 %! assert (u * s * v', a, sqrt (eps('single'))); |
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370 |
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371 %!test |
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372 %! a = single([1, 2; 3, 4; 5, 6]); |
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373 %! [u, s, v] = svd (a); |
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374 %! assert (u * s * v', a, sqrt (eps('single'))); |
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375 |
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376 %!test |
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377 %! a = single([1, 2, 3; 4, 5, 6]); |
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378 %! [u, s, v] = svd (a, 1); |
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379 %! assert (u * s * v', a, sqrt (eps('single'))); |
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380 |
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381 %!test |
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382 %! a = single([1, 2; 3, 4; 5, 6]); |
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383 %! [u, s, v] = svd (a, 1); |
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384 %! assert (u * s * v', a, sqrt (eps('single'))); |
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385 |
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386 %!test |
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387 %! a = zeros (0, 5); |
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388 %! [u, s, v] = svd (a); |
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389 %! assert (size (u), [0, 0]); |
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390 %! assert (size (s), [0, 5]); |
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391 %! assert (size (v), [5, 5]); |
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392 |
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393 %!test |
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394 %! a = zeros (5, 0); |
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395 %! [u, s, v] = svd (a, 1); |
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396 %! assert (size (u), [5, 0]); |
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397 %! assert (size (s), [0, 0]); |
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398 %! assert (size (v), [0, 0]); |
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399 |
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400 %!error <Invalid call to svd.*> svd (); |
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401 %!error <Invalid call to svd.*> svd ([1, 2; 4, 5], 2, 3); |
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402 %!error <Invalid call to svd.*> [u, v] = svd ([1, 2; 3, 4]); |
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403 |
2928 | 404 */ |
10601 | 405 |
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406 DEFUN_DLD (svd_driver, args, nargout, |
10601 | 407 "-*- texinfo -*-\n\ |
408 @deftypefn {Loadable Function} {@var{old} =} svd_driver (@var{new})\n\ | |
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409 Sets or queries the underlying @sc{lapack} driver used by svd.\n\ |
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410 Currently recognized are \"gesvd\" and \"gesdd\". Default is \"gesvd\".\n\ |
10601 | 411 @seealso{svd}\n\ |
412 @end deftypefn") | |
413 { | |
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414 static const char *driver_names[] = { "gesvd", "gesdd", 0 }; |
10601 | 415 |
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416 return SET_INTERNAL_VARIABLE_CHOICES (svd_driver, driver_names); |
10601 | 417 } |